Sperm navigation along helical paths in 3D chemoattractant landscapes

Interplay of chemotactic force, Péclet number, and dimensionality dictates the dynamics of auto-chemotactic chiral active droplets

In living and synthetic active matter systems, the constituents can self-propel and interact with each other and with the environment through various physicochemical mechanisms. Among these mechanisms, chemotactic and auto-chemotactic effects are widely observed. The impact of (auto-)chemotactic effects on achiral active matter has been a recent research focus. However, the influence of these effects on chiral active matter remains elusive. Here, we develop a Brownian dynamics model coupled with a diffusion equation to examine the dynamics of auto-chemotactic chiral active droplets in both quasi-two-dimensional (2D) and three-dimensional (3D) systems. By quantifying the droplet trajectory as a function of the dimensionless Péclet number and chemotactic strength, our simulations well reproduce the curling and helical trajectories of nematic droplets in a surfactant-rich solution reported by Krüger et al. [Phys. Rev. Lett. 117, 048003 (2016)]. The modeled curling trajectory in 2D exhibits an emergent chirality, also consistent with the experiment. We further show that the geometry of the chiral droplet trajectories, characterized by the pitch and diameter, can be used to infer the velocities of the droplet. Interestingly, we find that, unlike the achiral case, the velocities of chiral active droplets show dimensionality dependence: its mean instantaneous velocity is higher in 3D than in 2D, whereas its mean migration velocity is lower in 3D than in 2D. Taken together, our particle-based simulations provide new insights into the dynamics of auto-chemotactic chiral active droplets, reveal the effects of dimensionality, and pave the way toward their applications, such as drug delivery, sensors, and micro-reactors.

Viscous Loading Regulates the Flagellar Energetics of Human and Bull Sperm

The viscoelastic properties of the female reproductive tract influence sperm swimming behavior, but the exact role of these rheological changes in regulating sperm energetics remains unknown. Using high-speed dark-field microscopy, the flagellar dynamics of free-swimming sperm across a physiologically relevant range of viscosities is resolved. A transition from 3D to 2D slither swimming under an increased viscous loading is revealed, in the absence of any geometrical or chemical stimuli. This transition is species-specific, aligning with viscosity variations within each species' reproductive tract. Despite substantial drag increase, 2D slithering sperm maintain a steady swimming speed across a wide viscosity range (20-250 and 75-1000 mPa s for bull and human sperm) by dissipating over sixfold more energy into the fluid without elevating metabolic activity, potentially by altering the mechanisms of dynein motor activity. This energy-efficient motility mode is ideally suited for the viscous environment of the female reproductive tract.

Digital in-line holographic microscopy for label-free identification and tracking of biological cells

Digital in-line holographic microscopy (DIHM) is a non-invasive, real-time, label-free technique that captures three-dimensional (3D) positional, orientational, and morphological information from digital holographic images of living biological cells. Unlike conventional microscopies, the DIHM technique enables precise measurements of dynamic behaviors exhibited by living cells within a 3D volume. This review outlines the fundamental principles and comprehensive digital image processing procedures employed in DIHM-based cell tracking methods. In addition, recent applications of DIHM technique for label-free identification and digital tracking of various motile biological cells, including human blood cells, spermatozoa, diseased cells, and unicellular microorganisms, are thoroughly examined. Leveraging artificial intelligence has significantly enhanced both the speed and accuracy of digital image processing for cell tracking and identification. The quantitative data on cell morphology and dynamics captured by DIHM can effectively elucidate the underlying mechanisms governing various microbial behaviors and contribute to the accumulation of diagnostic databases and the development of clinical treatments.

What is it like to be a choanoflagellate? Sensation, processing and behavior in the closest unicellular relatives of animals

All animals evolved from a single lineage of unicellular precursors more than 600 million years ago. Thus, the biological and genetic foundations for animal sensation, cognition and behavior must necessarily have arisen by modifications of pre-existing features in their unicellular ancestors. Given that the single-celled ancestors of the animal kingdom are extinct, the only way to reconstruct how these features evolved is by comparing the biology and genomic content of extant animals to their closest living relatives. Here, we reconstruct the Umwelt (the subjective, perceptive world) inhabited by choanoflagellates, a group of unicellular (or facultatively multicellular) aquatic microeukaryotes that are the closest living relatives of animals. Although behavioral research on choanoflagellates remains patchy, existing evidence shows that they are capable of chemosensation, photosensation and mechanosensation. These processes often involve specialized sensorimotor cellular appendages (cilia, microvilli, and/or filopodia) that resemble those that underlie perception in most animal sensory cells. Furthermore, comparative genomics predicts an extensive "sensory molecular toolkit" in choanoflagellates, which both provides a potential basis for known behaviors and suggests the existence of a largely undescribed behavioral complexity that presents exciting avenues for future research. Finally, we discuss how facultative multicellularity in choanoflagellates might help us understand how evolution displaced the locus of decision-making from a single cell to a collective, and how a new space of behavioral complexity might have become accessible in the process.

Active oscillations in microscale navigation

Living organisms routinely navigate their surroundings in search of better conditions, more food, or to avoid predators. Typically, animals do so by integrating sensory cues from the environment with their locomotor apparatuses. For single cells or small organisms that possess motility, fundamental physical constraints imposed by their small size have led to alternative navigation strategies that are specific to the microscopic world. Intriguingly, underlying these myriad exploratory behaviours or sensory functions is the onset of periodic activity at multiple scales, such as the undulations of cilia and flagella, the vibrations of hair cells, or the oscillatory shape modes of migrating neutrophils. Here, I explore oscillatory dynamics in basal microeukaryotes and hypothesize that these active oscillations play a critical role in enhancing the fidelity of adaptive sensorimotor integration.

Steering undulatory micro-swimmers in a fluid flow through reinforcement learning

This work aims at finding optimal navigation policies for thin, deformable microswimmers that progress in a viscous fluid by propagating a sinusoidal undulation along their slender body. These active filaments are embedded in a prescribed, non-homogeneous flow, in which their swimming undulations have to compete with the drifts, strains, and deformations inflicted by the outer velocity field. Such an intricate situation, where swimming and navigation are tightly bonded, is addressed using various methods of reinforcement learning. Each swimmer has only access to restricted information on its configuration and has to select accordingly an action among a limited set. The optimisation problem then consists in finding the policy leading to the most efficient displacement in a given direction. It is found that usual methods do not converge and this pitfall is interpreted as a combined consequence of the non-Markovianity of the decision process, together with the highly chaotic nature of the dynamics, which is responsible for high variability in learning efficiencies. Still, we provide an alternative method to construct efficient policies, which is based on running several independent realisations of Q-learning. This allows the construction of a set of admissible policies whose properties can be studied in detail and compared to assess their efficiency and robustness.

Light, Matter, Action: Shining Light on Active Matter

Light carries energy and momentum. It can therefore alter the motion of objects on the atomic to astronomical scales. Being widely available, readily controllable, and broadly biocompatible, light is also an ideal tool to propel microscopic particles, drive them out of thermodynamic equilibrium, and make them active. Thus, light-driven particles have become a recent focus of research in the field of soft active matter. In this Perspective, we discuss recent advances in the control of soft active matter with light, which has mainly been achieved using light intensity. We also highlight some first attempts to utilize light's additional properties, such as its wavelength, polarization, and momentum. We then argue that fully exploiting light with all of its properties will play a critical role in increasing the level of control over the actuation of active matter as well as the flow of light itself through it. This enabling step will advance the design of soft active matter systems, their functionalities, and their transfer toward technological applications.

Escaping Behavior of Sperms on the Biomimetic Oviductal Surface

Before fertilization, sperms adhere to oviductal epithelium cells, and only a restrictive number of winner sperms can escape to reach the egg. To study the sperm escape behavior from the oviductal surface, we developed a microfluidic chip to fabricate an adhesive surface and to create a gradient of progesterone (P₄) for mimicking the oviduct microenvironment in vivo. We identified three sperm motion patterns in such a microenvironment─anchored spin, run-and-spin, and escaped mode. By using kinetic analysis, we verified the hypothesis that the responsive rotation energy anchored with the adhered sperm head determines whether the sperm is trapped or detaching, which is defined as the hammer flying strategy of successful escape after accumulating energy in the process of rotating. Intriguingly, this hammer-throw escaping is able to be triggered by the P₄ biochemical stimulation. Our results revealed the tangled process of sperm escape before fertilization in the ingenious microfluidic system.

Multi-Illumination Single-Holographic-Exposure Lensless Fresnel (MISHELF) Microscopy: Principles and Biomedical Applications

Lensless holographic microscopy (LHM) comes out as a promising label-free technique since it supplies high-quality imaging and adaptive magnification in a lens-free, compact and cost-effective way. Compact sizes and reduced prices of LHMs make them a perfect instrument for point-of-care diagnosis and increase their usability in limited-resource laboratories, remote areas, and poor countries. LHM can provide excellent intensity and phase imaging when the twin image is removed. In that sense, multi-illumination single-holographic-exposure lensless Fresnel (MISHELF) microscopy appears as a single-shot and phase-retrieved imaging technique employing multiple illumination/detection channels and a fast-iterative phase-retrieval algorithm. In this contribution, we review MISHELF microscopy through the description of the principles, the analysis of the performance, the presentation of the microscope prototypes and the inclusion of the main biomedical applications reported so far.

Hydrodynamic Synchronization of Chiral Microswimmers

We study synchronization in bulk suspensions of spherical microswimmers with chiral trajectories using large scale numerics. The model is generic. It corresponds to the lowest order solution of a general model for self-propulsion at low Reynolds numbers, consisting of a nonaxisymmetric rotating source dipole. We show that both purely circular and helical swimmers can spontaneously synchronize their rotation. The synchronized state corresponds to velocity alignment with high orientational order in both the polar and azimuthal directions. Finally, we consider a racemic mixture of helical swimmers where intraspecies synchronization is observed while the system remains as a spatially uniform fluid. Our results demonstrate hydrodynamic synchronization as a natural collective phenomenon for microswimmers with chiral trajectories.

Sea urchin sperm exploit extremum seeking control to find the egg

Sperm cells perform extremely demanding tasks with minimal capabilities. The cells must quickly navigate in a noisy environment to find an egg within a short time window for successful fertilization without any global positioning information. Many research efforts have been dedicated to derive mathematical principles that explain their superb navigation strategy. Here we show that the navigation strategy of sea urchin sperm, also known as helical klinotaxis, is a natural implementation of a well-established adaptive control paradigm known as extremum seeking. This bridge between control theory and the biology of taxis in microorganisms is expected to deepen our understanding of the process. For example, the formulation leads to a coarse-grained model of the signaling pathway that offers new insights on the peculiar switching-like behavior between high- and low-gain steering modes observed in sea urchin sperm. Moreover, it may guide engineers in developing bioinspired miniaturized robots with minimal sensors.

Assessment of sperm motility in livestock: Perspectives based on sperm swimming conditions in vivo

Evaluation of sperm motility is well-established in farm animals for quickly selecting ejaculates for semen processing into insemination doses and for evaluating the quality of preserved semen. Likewise, sperm motility is a fundamental parameter used by spermatologists in basic and applied science. Motility is commonly assessed using computer-assisted semen analysis (CASA). Recent increases in computational power, as well as utilization of mobile CASA systems and open-source CASA programs, broaden the possibilities for motility evaluation. Despite this technological progress, the potential of computer-generated motility data to assess male fertility remains challenging and may be limited. Relevance for fertility assessment could be improved if measurement conditions would more closely mimic the in vivo situation. Hence, this review is focused on the current trends of automated semen assessment in livestock and explores perspectives for future use with respect to the physiological and physical conditions encountered by sperm in the female reproductive tract. Validation of current CASA systems with more complex, microfluidic-based devices mimicking the female reproductive tract environment could improve the value of sperm kinematic data for assessing the fertilizing capacity of semen samples, not only for application in livestock but also for use in conducting assisted reproduction techniques in other species.

cAMP and the Fibrous Sheath Protein CABYR (Ca2+-Binding Tyrosine-Phosphorylation-Regulated Protein) Is Required for 4D Sperm Movement

A new life starts with successful fertilization whereby one sperm from a pool of millions fertilizes the oocyte. Sperm motility is one key factor for this selection process, which depends on a coordinated flagellar movement. The flagellar beat cycle is regulated by Ca2+ entry via CatSper, cAMP, Mg2+, ADP and ATP. This study characterizes the effects of these parameters for 4D sperm motility, especially for flagellar movement and the conserved clockwise (CW) path chirality of murine sperm. Therefore, we use detergent-extracted mouse sperm and digital holographic microscopy (DHM) to show that a balanced ratio of ATP to Mg2+ in addition with 18 µM cAMP and 1 mM ADP is necessary for controlled flagellar movement, induction of rolling along the long axis and CW path chirality. Rolling along the sperm’s long axis, a proposed mechanism for sperm selection, is absent in sea urchin sperm, lacking flagellar fibrous sheath (FS) and outer-dense fibers (ODFs). In sperm lacking CABYR, a Ca2+-binding tyrosine-phosphorylation regulated protein located in the FS, the swim path chirality is preserved. We conclude that specific concentrations of ATP, ADP, cAMP and Mg2+ as well as a functional CABYR play an important role for sperm motility especially for path chirality.

CatSper and its CaM-like Ca2+ sensor EFCAB9 are necessary for the path chirality of sperm

Successful fertilization depends on sperm motility adaptation. Ejaculated and activated sperm beat symmetrically in high frequency, move linearly, and swim with clockwise chirality. After capacitation, sperm beat asymmetrically with lower amplitude and a high lateral head excursion. This motility change called hyperactivation requires CatSper activation and an increase in intracellular Ca²⁺ . However, whether CatSper-mediated Ca²⁺ influx participates in controlling the swim path chirality is unknown. In this study, we show that the clockwise path chirality is preserved in mouse sperm regardless of capacitation state but is lost in the sperm either lacking the entire CatSper channel or its Ca²⁺ sensor EFCAB9. Pharmacological inhibition of CatSper with either mibefradil or NNC 55-0396 leads to the same loss in swim path chirality. Exposure of sperm to the recombinant N-terminal part of the zona pellucida protein 2 randomizes chirality in capacitated cells, but not in non-capacitated ones. We conclude that Ca²⁺ sensitive regulation of CatSper activity orchestrates clockwise swim path chirality of sperm and any substantial change, such as the physiological stimulus of zona pellucida glycoproteins, results in a loss of chirality.

Unraveling the Kinematics of Sperm Motion by Reconstructing the Flagellar Wave Motion in 3D

Sperm swim through the female reproductive tract by propagating a 3D flagellar wave that is self-regulatory in nature and driven by dynein motors. Traditional microscopy methods fail to capture the full dynamics of sperm flagellar activity as they only image and analyze sperm motility in 2D. Here, an automated platform to analyze sperm swimming behavior in 3D by using thin-lens approximation and high-speed dark field microscopy to reconstruct the flagellar waveform in 3D is presented. It is found that head-tethered mouse sperm exhibit a rolling beating behavior in 3D with the beating frequency of 6.2 Hz using spectral analysis. The flagellar waveform bends in 3D, particularly in the distal regions, but is only weakly nonplanar and ambidextrous in nature, with the local helicity along the flagellum fluctuating between clockwise and counterclockwise handedness. These findings suggest a nonpersistent flagellar helicity. This method provides new opportunities for the accurate measurement of the full motion of eukaryotic flagella and cilia which is essential for a biophysical understanding of their activation by dynein motors.

The tubulin code in mammalian sperm development and function

Microtubules are cytoskeletal elements that play key roles throughout the different steps of sperm development. As an integral part of the sperm flagellum, the molecular machine that generates sperm motility, microtubules are also essential for the progressive swimming of sperm to the oocyte, which is a prerequisite for fertilisation. Given the central role of microtubules in all steps of spermatogenesis, their functions need to be tightly controlled. Recent work has showcased tubulin posttranslational modifications as key players in sperm development and function, with aberrations often leading to male infertility with a broad spectrum of sperm defects. Posttranslational modifications are part of the tubulin code, a mechanism that can control microtubule functions by modulating the properties of their molecular building blocks, the tubulin proteins. Here we review the current knowledge on the implications of the tubulin code in sperm development and functions and its importance for male fertility.

Rotational Locomotion of an Active Gel Driven by Internal Chemical Signals

Chemical waves arising from coupled reaction and transport can serve as biomimetic "nerve signals" to study the underlying origin and regulation of active locomotion. During wave propagation in more than one spatial dimension, the propagation direction of spiral and pulse waves in a nanogel-based PAAm self-oscillating gel, i.e., the orientation of the driving force, may deviate from the normal direction to the wave fronts. Alternating forward and backward retrograde wave locomotion along the normal and tangential kinematic vectors with a phase difference leads to a curved path, i.e., rotational locomotion. This work indicates that appendages in an organism are not required for this type of locomotion. This locomotion mechanism reveals a general principle underlying the dynamical origin of biological helical locomotion and also suggests design approaches for complex locomotion of soft robots and smart materials.

Multiple functions of flagellar motility and chemotaxis in bacterial physiology

Most swimming bacteria are capable of following gradients of nutrients, signaling molecules and other environmental factors that affect bacterial physiology. This tactic behavior became one of the most-studied model systems for signal transduction and quantitative biology, and underlying molecular mechanisms are well characterized in Escherichia coli and several other model bacteria. In this review, we focus primarily on less understood aspect of bacterial chemotaxis, namely its physiological relevance for individual bacterial cells and for bacterial populations. As evident from multiple recent studies, even for the same bacterial species flagellar motility and chemotaxis might serve multiple roles, depending on the physiological and environmental conditions. Among these, finding sources of nutrients and more generally locating niches that are optimal for growth appear to be one of the major functions of bacterial chemotaxis, which could explain many chemoeffector preferences as well as flagellar gene regulation. Chemotaxis might also generally enhance efficiency of environmental colonization by motile bacteria, which involves intricate interplay between individual and collective behaviors and trade-offs between growth and motility. Finally, motility and chemotaxis play multiple roles in collective behaviors of bacteria including swarming, biofilm formation and autoaggregation, as well as in their interactions with animal and plant hosts.

Mammalian sperm hyperactivation regulates navigation via physical boundaries and promotes pseudo-chemotaxis

Mammalian sperm migration within the complex and dynamic environment of the female reproductive tract toward the fertilization site requires navigational mechanisms, through which sperm respond to the tract environment and maintain the appropriate swimming behavior. In the oviduct (fallopian tube), sperm undergo a process called "hyperactivation," which involves switching from a nearly symmetrical, low-amplitude, and flagellar beating pattern to an asymmetrical, high-amplitude beating pattern that is required for fertilization in vivo. Here, exploring bovine sperm motion in high-aspect ratio microfluidic reservoirs as well as theoretical and computational modeling, we demonstrate that sperm hyperactivation, in response to pharmacological agonists, modulates sperm-sidewall interactions and thus navigation via physical boundaries. Prior to hyperactivation, sperm remained swimming along the sidewalls of the reservoirs; however, once hyperactivation caused the intrinsic curvature of sperm to exceed a critical value, swimming along the sidewalls was reduced. We further studied the effect of noise in the intrinsic curvature near the critical value and found that these nonthermal fluctuations yielded an interesting "Run-Stop" motion on the sidewall. Finally, we observed that hyperactivation produced a "pseudo-chemotaxis" behavior, in that sperm stayed longer within microfluidic chambers containing higher concentrations of hyperactivation agonists.

Three-dimensional tracking of the ciliate Tetrahymena reveals the mechanism of ciliary stroke-driven helical swimming

Helical swimming in free-space is a common behavior among microorganisms, such as ciliates that are covered with thousands hair-like motile cilia, and is thought to be essential for cells to orient directly to an external stimulus. However, a direct quantification of their three-dimensional (3D) helical trajectories has not been reported, in part due to difficulty in tracking 3D swimming behavior of ciliates, especially Tetrahymena with a small, transparent cell body. Here, we conducted 3D tracking of fluorescent microbeads within a cell to directly visualize the helical swimming exhibited by Tetrahymena. Our technique showed that Tetrahymena swims along a right-handed helical path with right-handed rolling of its cell body. Using the Tetrahymena cell permeabilized with detergent treatment, we also observed that influx of Ca²⁺ into cilia changed the 3D-trajectory patterns of Tetrahymena swimming, indicating that the beating pattern of cilia is the determining factor in its swimming behavior.

Oblique circle method for measuring the curvature and twist of mitotic spindle microtubule bundles

The highly ordered spatial organization of microtubule bundles in the mitotic spindle is crucial for its proper functioning. The recent discovery of twisted shapes of microtubule bundles and spindle chirality suggests that the bundles extend along curved paths in three dimensions, rather than being confined to a plane. This, in turn, implies that rotational forces, i.e., torques, exist in the spindle in addition to the widely studied linear forces. However, studies of spindle architecture and forces are impeded by a lack of a robust method for the geometric quantification of microtubule bundles in the spindle. In this work, we describe a simple method for measuring and evaluating the shapes of microtubule bundles by characterizing them in terms of their curvature and twist. By using confocal microscopy, we obtain three-dimensional images of spindles, which allows us to trace the entire microtubule bundle. For each traced bundle, we first fit a plane and then fit a circle lying in that plane. With this robust method, we extract the curvature and twist, which represent the geometric information characteristic for each bundle. As the bundle shapes reflect the forces within them, this method is valuable for the understanding of forces that act on chromosomes during mitosis.

In Silico Reconstruction of Sperm Chemotaxis

In echinoderms, sperm swims in random circles and turns in response to a chemoattractant. The chemoattractant evokes transient Ca²⁺ influx in the sperm flagellum and induces turning behavior. Recently, the molecular mechanisms and biophysical properties of this sperm response have been clarified. Based on these experimental findings, in this study, we reconstructed a sperm model in silico to demonstrate an algorithm for sperm chemotaxis. We also focused on the importance of desensitizing the chemoattractant receptor in long-range chemotaxis because sperm approach distantly located eggs, and they must sense the chemoattractant concentration over a broad range. Using parameters of the sea urchin, simulations showed that a number of sperm could reach the egg from millimeter-order distances with desensitization, indicating that we could organize a functional sperm model, and that desensitization of the receptor is essential for sperm chemotaxis. Then, we compared the model with starfish sperm, which has a different desensitization scheme and analyzed the properties of the model against various disturbances. Our approach can be applied as a novel tool in chemotaxis research.

Multifocal imaging for precise, label-free tracking of fast biological processes in 3D

Many biological processes happen on a nano- to millimeter scale and within milliseconds. Established methods such as confocal microscopy are suitable for precise 3D recordings but lack the temporal or spatial resolution to resolve fast 3D processes and require labeled samples. Multifocal imaging (MFI) allows high-speed 3D imaging but is limited by the compromise between high spatial resolution and large field-of-view (FOV), and the requirement for bright fluorescent labels. Here, we provide an open-source 3D reconstruction algorithm for multi-focal images that allows using MFI for fast, precise, label-free tracking spherical and filamentous structures in a large FOV and across a high depth. We characterize fluid flow and flagellar beating of human and sea urchin sperm with a z-precision of 0.15 µm, in a volume of 240 × 260 × 21 µm, and at high speed (500 Hz). The sampling volume allowed to follow sperm trajectories while simultaneously recording their flagellar beat. Our MFI concept is cost-effective, can be easily implemented, and does not rely on object labeling, which renders it broadly applicable.

Modelling Motility: The Mathematics of Spermatozoa

In one of the first examples of how mechanics can inform axonemal mechanism, Machin's study in the 1950s highlighted that observations of sperm motility cannot be explained by molecular motors in the cell membrane, but would instead require motors distributed along the flagellum. Ever since, mechanics and hydrodynamics have been recognised as important in explaining the dynamics, regulation, and guidance of sperm. More recently, the digitisation of sperm videomicroscopy, coupled with numerous modelling and methodological advances, has been bringing forth a new era of scientific discovery in this field. In this review, we survey these advances before highlighting the opportunities that have been generated for both recent research and the development of further open questions, in terms of the detailed characterisation of the sperm flagellum beat and its mechanics, together with the associated impact on cell behaviour. In particular, diverse examples are explored within this theme, ranging from how collective behaviours emerge from individual cell responses, including how these responses are impacted by the local microenvironment, to the integration of separate advances in the fields of flagellar analysis and flagellar mechanics.

Reconstruction of the three-dimensional beat pattern underlying swimming behaviors of sperm

 The eukaryotic flagellum propels sperm cells and simultaneously detects physical and chemical cues that modulate the waveform of the flagellar beat. Most previous studies have characterized the flagellar beat and swimming trajectories in two space dimensions (2D) at a water/glass interface. Here, using refined holographic imaging methods, we report high-quality recordings of three-dimensional (3D) flagellar bending waves. As predicted by theory, we observed that an asymmetric and planar flagellar beat results in a circular swimming path, whereas a symmetric and non-planar flagellar beat results in a twisted-ribbon swimming path. During swimming in 3D, human sperm flagella exhibit torsion waves characterized by maxima at the low curvature regions of the flagellar wave. We suggest that these torsion waves are common in nature and that they are an intrinsic property of beating axonemes. We discuss how 3D beat patterns result in twisted-ribbon swimming paths. This study provides new insight into the axoneme dynamics, the 3D flagellar beat, and the resulting swimming behavior.

High-speed, three-dimensional imaging reveals chemotactic behaviour specific to human-infective Leishmania parasites

Cellular motility is an ancient eukaryotic trait, ubiquitous across phyla with roles in predator avoidance, resource access, and competition. Flagellar motility is seen in various parasitic protozoans, and morphological changes in flagella during the parasite life cycle have been observed. We studied the impact of these changes on motility across life cycle stages, and how such changes might serve to facilitate human infection. We used holographic microscopy to image swimming cells of different Leishmania mexicana life cycle stages in three dimensions. We find that the human-infective (metacyclic promastigote) forms display ‘run and tumble’ behaviour in the absence of stimulus, reminiscent of bacterial motion, and that they specifically modify swimming direction and speed to target host immune cells in response to a macrophage-derived stimulus. Non-infective (procyclic promastigote) cells swim more slowly, along meandering helical paths. These findings demonstrate adaptation of swimming phenotype and chemotaxis towards human cells.

Microgel that swims to the beat of light

Complementary to the quickly advancing understanding of the swimming of microorganisms, we demonstrate rather simple design principles for systems that can mimic swimming by body shape deformation. For this purpose, we developed a microswimmer that could be actuated and controlled by fast temperature changes through pulsed infrared light irradiation. The construction of the microswimmer has the following features: (i) it is a bilayer ribbon with a length of 80 or 120 [Formula: see text]m, consisting of a thermo-responsive hydrogel of poly-N-isopropylamide coated with a 2-nm layer of gold and equipped with homogeneously dispersed gold nanorods; (ii) the width of the ribbon is linearly tapered with a wider end of 5 [Formula: see text]m and a tip of 0.5 [Formula: see text]m; (iii) a thickness of only 1 and 2 [Formula: see text]m that ensures a maximum variation of the cross section of the ribbon along its length from square to rectangular. These wedge-shaped ribbons form conical helices when the hydrogel is swollen in cold water and extend to a filament-like object when the temperature is raised above the volume phase transition of the hydrogel at [Formula: see text]. The two ends of these ribbons undergo different but coupled modes of motion upon fast temperature cycling through plasmonic heating of the gel-objects from inside. Proper choice of the IR-light pulse sequence caused the ribbons to move at a rate of 6 body length/s (500 [Formula: see text]m/s) with the wider end ahead. Within the confinement of rectangular container of 30 [Formula: see text]m height and 300 [Formula: see text]m width, the different modes can be actuated in a way that the movement is directed by the energy input between spinning on the spot and fast forward locomotion.

Curvature in the reproductive tract alters sperm-surface interactions

The fallopian tube is lined with a highly complex folded epithelium surrounding a lumen that progressively narrows. To study the influence of this labyrinthine complexity on sperm behavior, we use droplet microfluidics to create soft curved interfaces over a range of curvatures corresponding to the in vivo environment. We reveal a dynamic response mechanism in sperm, switching from a progressive surface-aligned motility mode at low curvatures (larger droplets), to an aggressive surface-attacking mode at high curvatures (smaller droplets of <50 µm-radius). We show that sperm in the attacking mode swim ~33% slower, spend 1.66-fold longer at the interface and have a 66% lower beating amplitude than in the progressive mode. These findings demonstrate that surface curvature within the fallopian tube alters sperm motion from a faster surface aligned locomotion in distal regions to a prolonged physical contact with the epithelium near the site of fertilization, the latter being known to promote capacitation and fertilization competence.

Micromotor-mediated sperm constrictions for improved swimming performance

Sperm-driven micromotors, consisting of a single sperm cell captured in a microcap, utilize the strong propulsion generated by the flagellar beat of motile spermatozoa for locomotion. It enables the movement of such micromotors in biological media, while being steered remotely by means of an external magnetic field. The substantial decrease in swimming speed, caused by the additional hydrodynamic load of the microcap, limits the applicability of sperm-based micromotors. Therefore, to improve the performance of such micromotors, we first investigate the effects of additional cargo on the flagellar beat of spermatozoa. We designed two different kinds of microcaps, which each result in different load responses of the flagellar beat. As an additional design feature, we constrain rotational degrees of freedom of the cell's motion by modifying the inner cavity of the cap. Particularly, cell rolling is substantially reduced by tightly locking the sperm head inside the microcap. Likewise, cell yawing is decreased by aligning the micromotors under an external static magnetic field. The observed differences in swimming speed of different micromotors are not so much a direct consequence of hydrodynamic effects, but rather stem from changes in flagellar bending waves, hence are an indirect effect. Our work serves as proof-of-principle that the optimal design of microcaps is key for the development of efficient sperm-driven micromotors.

Sperm chemotaxis in marine species is optimal at physiological flow rates according theory of filament surfing

Sperm of marine invertebrates have to find eggs cells in the ocean. Turbulent flows mix sperm and egg cells up to the millimeter scale; below this, active swimming and chemotaxis become important. Previous work addressed either turbulent mixing or chemotaxis in still water. Here, we present a general theory of sperm chemotaxis inside the smallest eddies of turbulent flow, where signaling molecules released by egg cells are spread into thin concentration filaments. Sperm cells ‘surf’ along these filaments towards the egg. External flows make filaments longer, but also thinner. These opposing effects set an optimal flow strength. The optimum predicted by our theory matches flow measurements in shallow coastal waters. Our theory quantitatively agrees with two previous fertilization experiments in Taylor-Couette chambers and provides a mechanistic understanding of these early experiments. ‘Surfing along concentration filaments’ could be a paradigm for navigation in complex environments in the presence of turbulent flow.

Many motile cells navigate in complex environments along concentration gradients of signaling molecules. This chemotaxis has been studied extensively both experimentally and theoretically, yet mostly for idealized conditions of perfect chemical gradients. But under physiological conditions, concentration fields are subject to distortions, e.g., by turbulent flows in the ocean. Pioneering experiments suggest that in species with external fertilization, chemotaxis of sperm cells towards the egg may even work better at an optimal flow strength compared to conditions of still water. Yet to date, the mechanistic cause for this optimum is not known. We present a general theory of chemotactic navigation in external flow. We characterize how external flow distorts concentration fields into long filaments, and show how chemotaxing cells can subsequently ‘surf’ along these filaments towards a chemoattractant source. Stronger flows make concentration filaments longer, but also thinner; together, these two counter-acting effects set an optimal flow strength. Beyond fertilization of marine invertebrates, we believe that ‘surfing along concentration filaments’ could be a more general paradigm, relevant also for the ecology of marine bacteria feeding on organic marine snow in the ocean, or chemotaxis inside multi-cellular organisms with internal flows.

How Euglena gracilis swims: Flow field reconstruction and analysis

Euglena gracilis is a unicellular organism that swims by beating a single anterior flagellum. We study the nonplanar waveforms spanned by the flagellum during a swimming stroke and the three-dimensional flows that they generate in the surrounding fluid. Starting from a small set of time-indexed images obtained by optical microscopy on a swimming Euglena cell, we construct a numerical interpolation of the stroke. We define an optimal interpolation (which we call synthetic stroke) by minimizing the discrepancy between experimentally measured velocities (of the swimmer) and those computed by solving numerically the equations of motion of the swimmer driven by the trial interpolated stroke. The good match we obtain between experimentally measured and numerically computed trajectories provides a first validation of our synthetic stroke. We further validate the procedure by studying the flow velocities induced in the surrounding fluid. We compare the experimentally measured flow fields with the corresponding quantities computed by solving numerically the Stokes equations for the fluid flow, in which the forcing is provided by the synthetic stroke, and find good matching. Finally, we use the synthetic stroke to derive a coarse-grained model of the flow field resolved in terms of a few dominant singularities. The far field is well approximated by a time-varying Stresslet, and we show that the average behavior of Euglena during one stroke is that of an off-axis puller. The reconstruction of the flow field closer to the swimmer body requires a more complex system of singularities. A system of two Stokeslets and one Rotlet, that can be loosely associated with the force exerted by the flagellum, the drag of the body, and a torque to guarantee rotational equilibrium, provides a good approximation.

Origins of eukaryotic excitability

All living cells interact dynamically with a constantly changing world. Eukaryotes, in particular, evolved radically new ways to sense and react to their environment. These advances enabled new and more complex forms of cellular behaviour in eukaryotes, including directional movement, active feeding, mating, and responses to predation. But what are the key events and innovations during eukaryogenesis that made all of this possible? Here we describe the ancestral repertoire of eukaryotic excitability and discuss five major cellular innovations that enabled its evolutionary origin. The innovations include a vastly expanded repertoire of ion channels, the emergence of cilia and pseudopodia, endomembranes as intracellular capacitors, a flexible plasma membrane and the relocation of chemiosmotic ATP synthesis to mitochondria, which liberated the plasma membrane for more complex electrical signalling involved in sensing and reacting. We conjecture that together with an increase in cell size, these new forms of excitability greatly amplified the degrees of freedom associated with cellular responses, allowing eukaryotes to vastly outperform prokaryotes in terms of both speed and accuracy. This comprehensive new perspective on the evolution of excitability enriches our view of eukaryogenesis and emphasizes behaviour and sensing as major contributors to the success of eukaryotes. This article is part of the theme issue 'Basal cognition: conceptual tools and the view from the single cell'.

Tubulin glycylation controls axonemal dynein activity, flagellar beat, and male fertility

Posttranslational modifications of the microtubule cytoskeleton have emerged as key regulators of cellular functions, and their perturbations have been linked to a growing number of human pathologies. Tubulin glycylation modifies microtubules specifically in cilia and flagella, but its functional and mechanistic roles remain unclear. In this study, we generated a mouse model entirely lacking tubulin glycylation. Male mice were subfertile owing to aberrant beat patterns of their sperm flagella, which impeded the straight swimming of sperm cells. Using cryo-electron tomography, we showed that lack of glycylation caused abnormal conformations of the dynein arms within sperm axonemes, providing the structural basis for the observed dysfunction. Our findings reveal the importance of microtubule glycylation for controlled flagellar beating, directional sperm swimming, and male fertility.

The anatomy, movement, and functions of human sperm tail: an evolving mystery

Sperms have attracted attention of many researchers since it was discovered by Antonie van Leeuwenhoek in 1677. Though a small cell, its every part has complex structure and different function to play in carrying life. Sperm tail is most complicated structure with more than 1000 proteins involved in its functioning. With the advent of three-dimensional microscopes, many studies are undergoing to understand exact mechanism of sperm tail movement. Most recent studies have shown that sperms move by spinning rather than swimming. Each subunit of tail, including axonemal, peri-axonemal structures, plays essential roles in sperm motility, capacitation, hyperactivation, fertilization. Furthermore, over 2300 genes are involved in spermatogenesis. A number of genetic mutations have been linked with abnormal sperm flagellar development leading to motility defects and male infertility. It was found that 6% of male infertility cases are related to genetic causes, and 4% of couples undergoing intracytoplasmic sperm injection for male subfertility have chromosomal abnormalities. Hence, an understanding of sperm tail development and genes associated with its normal functioning can help in better diagnosis of male infertility and its management. There is still a lot that needs to be discovered about genes, proteins contributing to normal human sperm tail development, movement, and role in male fertility. Sperm tail has complex anatomy, with surrounding axoneme having 9 + 2 microtubules arrangement along its entire length and peri-axonemal structures that contribute in sperm motility and fertilization. In future sperm tail-associated genes, proteins and subunits can be used as markers of male fertility.

Flagellar kinematics reveals the role of environment in shaping sperm motility

Swimming spermatozoa from diverse organisms often have very similar morphologies, yet different motilities as a result of differences in the flagellar waveforms used for propulsion. The origin of these differences has remained largely unknown. Using high-speed video microscopy and mathematical analysis of flagellar shape dynamics, we quantitatively compare sperm flagellar waveforms from marine invertebrates to humans by means of a novel phylokinematic tree. This new approach revealed that genetically dissimilar sperm can exhibit strikingly similar flagellar waveforms and identifies two dominant flagellar waveforms among the deuterostomes studied here, corresponding to internal and external fertilizers. The phylokinematic tree shows marked discordance from the phylogenetic tree, indicating that physical properties of the fluid environment, more than genetic relatedness, act as an important selective pressure in shaping the evolution of sperm motility. More broadly, this work provides a physical axis to complement morphological and genetic studies to understand evolutionary relationships.

Haloarchaea swim slowly for optimal chemotactic efficiency in low nutrient environments

Archaea have evolved to survive in some of the most extreme environments on earth. Life in extreme, nutrient-poor conditions gives the opportunity to probe fundamental energy limitations on movement and response to stimuli, two essential markers of living systems. Here we use three-dimensional holographic microscopy and computer simulations to reveal that halophilic archaea achieve chemotaxis with power requirements one hundred-fold lower than common eubacterial model systems. Their swimming direction is stabilised by their flagella (archaella), enhancing directional persistence in a manner similar to that displayed by eubacteria, albeit with a different motility apparatus. Our experiments and simulations reveal that the cells are capable of slow but deterministic chemotaxis up a chemical gradient, in a biased random walk at the thermodynamic limit.

Emergent three-dimensional sperm motility: coupling calcium dynamics and preferred curvature in a Kirchhoff rod model

Changes in calcium concentration along the sperm flagellum regulate sperm motility and hyperactivation, characterized by an increased flagellar bend amplitude and beat asymmetry, enabling the sperm to reach and penetrate the ovum (egg). The signalling pathways by which calcium increases within the flagellum are well established. However, the exact mechanisms of how calcium regulates flagellar bending are still under investigation. We extend our previous model of planar flagellar bending by developing a fluid-structure interaction model that couples the 3D motion of the flagellum in a viscous Newtonian fluid with the evolving calcium concentration. The flagellum is modelled as a Kirchhoff rod: an elastic rod with preferred curvature and twist. The calcium dynamics are represented as a 1D reaction-diffusion model on a moving domain, the flagellum. The two models are coupled assuming that the preferred curvature and twist of the sperm flagellum depend on the local calcium concentration. To investigate the effect of calcium on sperm motility, we compare model results of flagellar bend amplitude and swimming speed for three cases: planar, helical (spiral with equal amplitude in both directions), and quasi-planar (spiral with small amplitude in one direction). We observe that for the same parameters, the planar swimmer is faster and a turning motion is more clearly observed when calcium coupling is accounted for in the model. In the case of flagellar bending coupled to the calcium concentration, we observe emergent trajectories that can be characterized as a hypotrochoid for both quasi-planar and helical bending.

Human sperm uses asymmetric and anisotropic flagellar controls to regulate swimming symmetry and cell steering

Flagellar beating drives sperm through the female reproductive tract and is vital for reproduction. Flagellar waves are generated by thousands of asymmetric molecular components; yet, paradoxically, forward swimming arises via symmetric side-to-side flagellar movement. This led to the preponderance of symmetric flagellar control hypotheses. However, molecular asymmetries must still dictate the flagellum and be manifested in the beat. Here, we reconcile molecular and microscopic observations, reconnecting structure to function, by showing that human sperm uses asymmetric and anisotropic controls to swim. High-speed three-dimensional (3D) microscopy revealed two coactive transversal controls: An asymmetric traveling wave creates a one-sided stroke, and a pulsating standing wave rotates the sperm to move equally on all sides. Symmetry is thus achieved through asymmetry, creating the optical illusion of bilateral symmetry in 2D microscopy. This shows that the sperm flagellum is asymmetrically controlled and anisotropically regularized by fast-signal transduction. This enables the sperm to swim forward.

Active dipolar spheroids in shear flow and transverse field: Population splitting, cross-stream migration, and orientational pinning

We study the steady-state behavior of active, dipolar, Brownian spheroids in a planar channel subjected to an imposed Couette flow and an external transverse field, applied in the "downward" normal-to-flow direction. The field-induced torque on active spheroids (swimmers) is taken to be of magnetic form by assuming that they have a permanent magnetic dipole moment, pointing along their self-propulsion (swim) direction. Using a continuum approach, we show that a host of behaviors emerges over the parameter space spanned by the particle aspect ratio, self-propulsion and shear/field strengths, and the channel width. The cross-stream migration of the model swimmers is shown to involve a regime of linear response (quantified by a linear-response factor) in weak fields. For prolate swimmers, the weak-field behavior crosses over to a regime of full swimmer migration to the bottom half of the channel in strong fields. For oblate swimmers, a counterintuitive regime of reverse migration arises in intermediate fields, where a macroscopic fraction of swimmers reorient and swim to the top channel half at an acute "upward" angle relative to the field axis. The diverse behaviors reported here are analyzed based on the shear-induced population splitting (bimodality) of the swim orientation, giving two distinct, oppositely polarized, swimmer subpopulations (albeit very differently for prolate/oblate swimmers) in each channel half. In strong fields, swimmers of both types exhibit net upstream currents relative to the laboratory frame. The onsets of full migration and net upstream current depend on the aspect ratio, enabling efficient particle separation strategies in microfluidic setups.

Flow-induced buckling dynamics of sperm flagella

The swimming sperm of many external fertilizing marine organisms face complex fluid flows during their search for egg cells. Aided by chemotaxis, relatively weak flows are known to enhance sperm-egg fertilization rates through hydrodynamic guidance. However, strong flows have the potential to mechanically inhibit flagellar motility through elastohydrodynamic interactions-a phenomenon that remains poorly understood. Here we explore the effects of flow on the buckling dynamics of sperm flagella in an extensional flow through detailed numerical simulations, which are informed by microfluidic experiments and high-speed imaging. Compressional fluid forces lead to rich buckling dynamics of the sperm flagellum beyond a critical dimensionless sperm number, Sp, which represents the ratio of viscous force to elastic force. For nonmotile sperm, the maximum buckling curvature and the number of buckling locations, or buckling mode, increase with increasing sperm number. In contrast, motile sperm exhibit a local flagellar curvature due to the propagation of bending waves along the flagellum. In compressional flow, this preexisting curvature acts as a precursor for buckling, which enhances local curvature without creating new buckling modes and leads to asymmetric beating. However, in extensional flow, flagellar beating remains symmetric with a smaller head yawing amplitude due to tensile forces. The flagellar beating frequency also influences the maximum curvature of motile sperm by facilitating sperm reorientation relative to the compressional axis of the flow near stagnation points. These combined simulations and experiments directly illustrate the microscopic elastohydrodynamic mechanisms responsible for inhibiting flagellar motility in flow and have possible implications for our understanding of external fertilization in dynamic marine systems.

Optimal actuation of flagellar magnetic microswimmers

We present an automated procedure for the design of optimal actuation for flagellar magnetic microswimmers based on numerical optimization. Using this method, a magnetic actuation method is provided which allows these devices to swim significantly faster compared to the usual sinusoidal actuation. This leads to a novel swimming strategy which makes the swimmer perform a three-dimensional figure-eight trajectory. This shows that a faster propulsion is obtained when the swimmer is allowed to go out of plane. This approach is experimentally validated on a scaled-up flexible swimmer.

The 2020 motile active matter roadmap

Activity and autonomous motion are fundamental in living and engineering systems. This has stimulated the new field of 'active matter' in recent years, which focuses on the physical aspects of propulsion mechanisms, and on motility-induced emergent collective behavior of a larger number of identical agents. The scale of agents ranges from nanomotors and microswimmers, to cells, fish, birds, and people. Inspired by biological microswimmers, various designs of autonomous synthetic nano- and micromachines have been proposed. Such machines provide the basis for multifunctional, highly responsive, intelligent (artificial) active materials, which exhibit emergent behavior and the ability to perform tasks in response to external stimuli. A major challenge for understanding and designing active matter is their inherent nonequilibrium nature due to persistent energy consumption, which invalidates equilibrium concepts such as free energy, detailed balance, and time-reversal symmetry. Unraveling, predicting, and controlling the behavior of active matter is a truly interdisciplinary endeavor at the interface of biology, chemistry, ecology, engineering, mathematics, and physics. The vast complexity of phenomena and mechanisms involved in the self-organization and dynamics of motile active matter comprises a major challenge. Hence, to advance, and eventually reach a comprehensive understanding, this important research area requires a concerted, synergetic approach of the various disciplines. The 2020 motile active matter roadmap of Journal of Physics: Condensed Matter addresses the current state of the art of the field and provides guidance for both students as well as established scientists in their efforts to advance this fascinating area.

High-resolution 4-D acquisition of freely swimming human sperm cells without staining

We present a new acquisition method that enables high-resolution, fine-detail full reconstruction of the three-dimensional movement and structure of individual human sperm cells swimming freely. We achieve both retrieval of the three-dimensional refractive-index profile of the sperm head, revealing its fine internal organelles and time-varying orientation, and the detailed four-dimensional localization of the thin, highly-dynamic flagellum of the sperm cell. Live human sperm cells were acquired during free swim using a high-speed off-axis holographic system that does not require any moving elements or cell staining. The reconstruction is based solely on the natural movement of the sperm cell and a novel set of algorithms, enabling the detailed four-dimensional recovery. Using this refractive-index imaging approach, we believe that we have detected an area in the cell that is attributed to the centriole. This method has great potential for both biological assays and clinical use of intact sperm cells.

Chemokinetic Scattering, Trapping, and Avoidance of Active Brownian Particles

We present a theory of chemokinetic search agents that regulate directional fluctuations according to distance from a target. A dynamic scattering effect reduces the probability to penetrate regions with high fluctuations and thus reduces search success for agents that respond instantaneously to positional cues. In contrast, agents with internal states that initially suppress chemokinesis can exploit scattering to increase their probability to find the target. Using matched asymptotics between the case of diffusive and ballistic search, we obtain analytic results beyond Fox colored noise approximation.

Sperm chemotaxis is driven by the slope of the chemoattractant concentration field

Spermatozoa of marine invertebrates are attracted to their conspecific female gamete by diffusive molecules, called chemoattractants, released from the egg investments in a process known as chemotaxis. The information from the egg chemoattractant concentration field is decoded into intracellular Ca²⁺ concentration ([Ca²⁺]_i) changes that regulate the internal motors that shape the flagellum as it beats. By studying sea urchin species-specific differences in sperm chemoattractant-receptor characteristics we show that receptor density constrains the steepness of the chemoattractant concentration gradient detectable by spermatozoa. Through analyzing different chemoattractant gradient forms, we demonstrate for the first time that Strongylocentrotus purpuratus sperm are chemotactic and this response is consistent with frequency entrainment of two coupled physiological oscillators: i) the stimulus function and ii) the [Ca²⁺]_i changes. We demonstrate that the slope of the chemoattractant gradients provides the coupling force between both oscillators, arising as a fundamental requirement for sperm chemotaxis.

Modular analysis of the control of flagellar Ca2+-spike trains produced by CatSper and CaV channels in sea urchin sperm

Intracellular calcium ([Ca²⁺]_i) is a basic and ubiquitous cellular signal controlling a wide variety of biological processes. A remarkable example is the steering of sea urchin spermatozoa towards the conspecific egg by a spatially and temporally orchestrated series of [Ca²⁺]_i spikes. Although this process has been an experimental paradigm for reproduction and sperm chemotaxis studies, the composition and regulation of the signalling network underlying the cytosolic calcium fluctuations are hitherto not fully understood. Here, we used a differential equations model of the signalling network to assess which set of channels can explain the characteristic envelope and temporal organisation of the [Ca²⁺]_i-spike trains. The signalling network comprises an initial membrane hyperpolarisation produced by an Upstream module triggered by the egg-released chemoattractant peptide, via receptor activation, cGMP synthesis and decay. Followed by downstream modules leading to intraflagellar pH (pH_i), voltage and [Ca²⁺]_i fluctuations. The Upstream module outputs were fitted to kinetic data on cGMP activity and early membrane potential changes measured in bulk cell populations. Two candidate modules featuring voltage-dependent Ca²⁺-channels link these outputs to the downstream dynamics and can independently explain the typical decaying envelope and the progressive spacing of the spikes. In the first module, [Ca²⁺]_i-spike trains require the concerted action of a classical Ca_V-like channel and a potassium channel, BK (Slo1), whereas the second module relies on pH_i-dependent CatSper dynamics articulated with voltage-dependent neutral sodium-proton exchanger (NHE). We analysed the dynamics of these two modules alone and in mixed scenarios. We show that the [Ca²⁺]_i dynamics observed experimentally after sustained alkalinisation can be reproduced by a model featuring the CatSper and NHE module but not by those including the pH-independent Ca_V and BK module or proportionate mixed scenarios. We conclude in favour of the module containing CatSper and NHE and highlight experimentally testable predictions that would corroborate this conclusion.

Fertilisation in marine invertebrates, such as the sea urchin, occurs during broadcast spawning events in which males and females of co-localised species ejaculate sperm and spawn eggs synchronously. During these events, spermatozoa have to find and fertilise conspecific eggs in the midst of all the other ones, which is a remarkable navigation and mating choice achievement. Sperm cells do this by navigating towards the source of species-specific peptides released by the egg, steered by spatial and temporally orchestrated peaks in intracellular calcium concentration that trigger sudden reorientations. How these calcium spikes are regulated and timed remains elusive. Different calcium channels have been implicated by indirect experimental evidence giving rise to a complex network of putative interacting components. We gained insight into the structure and function of this network by modelling it as a set of candidate modules that could be studied separately. By using this ‘divide and conquer’ approach to the complexity of the network, we could characterise the potential dynamics of each module and confront these dynamics with specific quantitative data. Our results indicate that the channel mediating calcium signals in sea urchin sperm is likely CatSper, a calcium channel necessary for human male fertility.

Synchrony and symmetry-breaking in active flagellar coordination

Living creatures exhibit a remarkable diversity of locomotion mechanisms, evolving structures specialized for interacting with their environment. In the vast majority of cases, locomotor behaviours such as flying, crawling and running are orchestrated by nervous systems. Surprisingly, microorganisms can enact analogous movement gaits for swimming using multiple, fast-moving cellular protrusions called cilia and flagella. Here, I demonstrate intermittency, reversible rhythmogenesis and gait mechanosensitivity in algal flagella, to reveal the active nature of locomotor patterning. In addition to maintaining free-swimming gaits, I show that the algal flagellar apparatus functions as a central pattern generator that encodes the beating of each flagellum in a network in a distinguishable manner. The latter provides a novel symmetry-breaking mechanism for cell reorientation. These findings imply that the capacity to generate and coordinate complex locomotor patterns does not require neural circuitry but rather the minimal ingredients are present in simple unicellular organisms. This article is part of the Theo Murphy meeting issue 'Unity and diversity of cilia in locomotion and transport'.

High-speed motility originates from cooperatively pushing and pulling flagella bundles in bilophotrichous bacteria

Bacteria propel and change direction by rotating long, helical filaments, called flagella. The number of flagella, their arrangement on the cell body and their sense of rotation hypothetically determine the locomotion characteristics of a species. The movement of the most rapid microorganisms has in particular remained unexplored because of additional experimental limitations. We show that magnetotactic cocci with two flagella bundles on one pole swim faster than 500 µm·s⁻¹ along a double helical path, making them one of the fastest natural microswimmers. We additionally reveal that the cells reorient in less than 5 ms, an order of magnitude faster than reported so far for any other bacteria. Using hydrodynamic modeling, we demonstrate that a mode where a pushing and a pulling bundle cooperate is the only possibility to enable both helical tracks and fast reorientations. The advantage of sheathed flagella bundles is the high rigidity, making high swimming speeds possible.

Rotational motion and rheotaxis of human sperm do not require functional CatSper channels and transmembrane Ca2+ signaling

Navigation of sperm in fluid flow, called rheotaxis, provides long‐range guidance in the mammalian oviduct. The rotation of sperm around their longitudinal axis (rolling) promotes rheotaxis. Whether sperm rolling and rheotaxis require calcium (Ca²⁺) influx via the sperm‐specific Ca²⁺ channel CatSper, or rather represent passive biomechanical and hydrodynamic processes, has remained controversial. Here, we study the swimming behavior of sperm from healthy donors and from infertile patients that lack functional CatSper channels, using dark‐field microscopy, optical tweezers, and microfluidics. We demonstrate that rolling and rheotaxis persist in CatSper‐deficient human sperm. Furthermore, human sperm undergo rolling and rheotaxis even when Ca²⁺ influx is prevented. Finally, we show that rolling and rheotaxis also persist in mouse sperm deficient in both CatSper and flagellar Ca²⁺‐signaling domains. Our results strongly support the concept that passive biomechanical and hydrodynamic processes enable sperm rolling and rheotaxis, rather than calcium signaling mediated by CatSper or other mechanisms controlling transmembrane Ca²⁺ flux.

Motility Analysis of Trypanosomatids

Motility analysis of microswimmers has long been limited to a few model cell types and broadly restricted by technical challenges of high-resolution in vivo microscopy. Recently, interdisciplinary interest in detailed analysis of the motile behavior of various species has gained momentum. Here we describe a basic protocol for motility analysis of an important, highly diverse group of eukaryotic flagellate microswimmers, using high spatiotemporal resolution videomicroscopy. Further, we provide a special, time-dependent tomographic approach for the proof of rotational locomotion of periodically oscillating microswimmers, using the same data. Taken together, the methods describe part of an integrative approach to generate decisive information on three-dimensional in vivo motility from standard two-dimensional videomicroscopy data.